CAJ | 학술논문

在各种波长调制光谱理论中，波长调制函数的形式一般是随时间变化的正弦函数，而在实际应用中，标准的正弦函数信号容易混入高次谐频而失真，从而给系统引入误差。理论研究了当正弦波长调制函数中混入二倍频项时洛伦兹线型的傅里叶级数，推导了该条件下洛伦兹线型的 N阶傅里叶系数的表达式。表达式中引入了谐波失真度参数 K以表示二次倍频分量与基频的比值，并针对 K＞0.01与 K＜0.01情况分别作了数值仿真，仿真结果表明：当 K小于0.01时，正弦调制函数的谐波失真带来的影响可以忽略，当K接近或高于0.1时，则会导致洛伦兹线型傅里叶级数幅度曲线中心点偏离原点，并且谐波曲线的阶次越高，或谐波失真度越大，曲线的偏离程度越严重。另外，仿真了在K大于0.01时，不同的调制度对奇数和偶数阶谐波幅度曲线的影响，结果表明存在一个最佳的调制度可以使谐波失真对正弦波长调制的影响最小。结果有利于加深对波长调制光谱的认识，对激光稳频技术也有重要的参考作用。
재각충파장조제광보이론중，파장조제함수적형식일반시수시간변화적정현함수，이재실제응용중，표준적정현함수신호용역혼입고차해빈이실진，종이급계통인입오차。이론연구료당정현파장조제함수중혼입이배빈항시락륜자선형적부리협급수，추도료해조건하락륜자선형적 N계부리협계수적표체식。표체식중인입료해파실진도삼수 K이표시이차배빈분량여기빈적비치，병침대 K＞0.01여 K＜0.01정황분별작료수치방진，방진결과표명：당 K소우0.01시，정현조제함수적해파실진대래적영향가이홀략，당K접근혹고우0.1시，칙회도치락륜자선형부리협급수폭도곡선중심점편리원점，병차해파곡선적계차월고，혹해파실진도월대，곡선적편리정도월엄중。령외，방진료재K대우0.01시，불동적조제도대기수화우수계해파폭도곡선적영향，결과표명존재일개최가적조제도가이사해파실진대정현파장조제적영향최소。결과유리우가심대파장조제광보적인식，대격광은빈기술야유중요적삼고작용。
In the present work ,the Fourier analysis of Lorentzian line shape broadened by non-sinusoidal wavelength modulation was investigated ,in which the third order and above harmonic items were ignored .The analytical expression of n-order Fourier coefficient was brought out ,where a variable K named harmonic distortion to characterize the ratio of the second harmonic to the first harmonic was introduced .Numerical simulations based on the cases of K>0.01 and K<0.01 were carried out ,and the re-sult shows :non-sinusoidal modulation has little effect compared with the sinusoidal modulation when K value is less than 0.01 , however ,if K value is about 0.1 or higher ,the center of the Fourier amplitude curve would deviate from the origin of coordi-nates .With the increase in the harmonic distortion ,the deviation of the curve grows ,and high order harmonics are more sensi-tive to the non-sinusoidal modulation compared with the low order harmonics .In addition ,when harmonic distortion cannot be ignored ,for example K>0.01 ,the effect of different depths of modulation on the odd and even order harmonic amplitude curve is significant .And the numerical simulation shows there exists an optimum value of modulation depth which could minimize the impact of the harmonic distortion ,and both large K value and small K value would cause a great error .The conclusion of this work could be applied in error analysis of wavelength modulation spectroscopy system .And the results are helpful to deepening understanding of WMS and would be the important reference for some kind of frequency stabilization technology in laser instru-ment .